So I'm a curious guy, I observe my universe, read about string theory, things like that. When I look around and see how everything works, I start to see some connections with common everyday occurrences and things we still have yet to explain. If it wasn't for those two books, being Hyperspace by Michio Kaku, and The Elegant Universe by Brian Greene, I would have totally missed out.

There's something interesting I notice about accelerating in a car. Of course, if your talking about a 120 hp civic you may not notice that much of a pull. But, if you own or have ever been for a ride in a quick sports car, then you know about the strong pull of "artificial" gravity that is created when the thing takes off. So, what we have going on here is that a car is increasing speed in a straight line. No change of direction, just taking off after waiting for the light to change, and accelerating to 50 mph.

Another way to generate this "artificial" gravity is by driving a constant speed around a corner. Given the curve is sharp enough, or you're going fast enough, you will feel a strong pull. Except this time, it's in a perpendicular direction to straight line acceleration. If you turned your seat to face right and took a fast right turn, you would feel the exact same thing as straight line acceleration. Another good example is the well known Vomit Comet, the airplane that gives you free fall for 45 seconds inside. This craft is taking a curved trajectory and generating the pull that cancels or doubles gravity. So, to recap once again, we have two scenarios where changing directions a constant speed around a curve creates a pulling force. It is not necessary to be changing speed for this to take effect.

Which brings me back to straight line acceleration. In two scenarios above, we made a pulling force by taking a curved path at constant speed, thus changing direction. So, when we feel this strange force when increasing speed in a straight line, what's going on here? How can this be? Well, the secret is that we are going around a curve in time. That is, changing direction in time and pointing ourselves in a direction towards space, ever so slightly. Keep in mind that we do not have to be changing speed, only changing direction along a curve to feel this force. When we travel around this temporal bend in the highway, we feel the cornering force as straight line acceleration. The momentum we carry during acceleration is angular momentum. And there it is, hidden in plain sight for every one to see. A fourth direction that we move in at a constant speed.

This brings me to a curious question: what is the constant speed that we are travelling through time? There can only be one answer to that one, and it has to be the speed of light, c. When we sit still at a traffic light, we have zero displacement in space. This is similar to driving due north, you have no east-west displacement. By taking a corner and driving NE, we feel this pull of acceleration, change our direction and add some displacement going east. We travel less distance going north now because we have given it to going east. So, if the magnitude of our vector through time is c, then changing direction in time and going around a corner will point us towards space. Pointing towards space is how we move, by removing our speed through time and adding it to space. This is how Einstein's Theory of Relativity fits in. The faster we go in space, the slower we move through time. Rotating the vector and reaching the speed of light in space means we remove all displacement through time. This is infinite velocity since travelling x miles in 0 hours is x/0, no solution, infinitely large.

But of course, there's the problem with Special Relativity. Reaching the speed of light means the mass of our atoms increase. And the faster we go, the heavier we get, thus making it harder to accelerate. Of course, this effect won't happen until one gets close to c. We're still free to travel at least a couple hundred million mph with no ill effects. Many have said that it's really the increase in electromagnetic mass from charged particles. But there's something interesting I see about the compactified dimesnions in String Theory. These tiny curled up extensions are embedded into every point of the common 4-D universe. This means travelling in a straight line will also circumnavigate the self repeating spaces trillions of times over. I'd like to refer back the old analogy of gravity as a bowling ball on a rubber sheet. Since the ball is heavy, it puts a big dent in it's space-time. This causes other objects to be attracted to it, being pulled by it's analogous gravity well. A canon ball is heavier and so will make a bigger dent. This can be interpreted as the wave function of mass. A taller wave height means more mass.

So, let's take this rubber sheet and curl it up so we can join the ends. Now, inside this rubber tube is where the bowling ball is rolling around in a circle. This is a simplified version of moving through the compactified Calabi-Yau manifold. Since travelling a straight line also cycles around the curved extensions, the bowling ball circles around inside the tube by analogy. Picking up speed effects both the extended and curled up. A curious side effect of the ball going faster around inside is that angular momentum increases and will bulge the ball further out. This is identical to the wave function of mass, since a taller wave is a heavier one. By starting with the rest mass wave height, we have increased the height by an increase in velocity. At the speed of light, something has to give and may be some sort of Calabi-Yau escape velocity. The rubber sheet of space-time tears and releases the atoms, terribly lorentz contracted and time and mass dilated.

From this theory I have come up with an interesting method for explaining the Quantum Foam on the Plank scale. This is where space and time break down, and pure energy can be taken out on a short term loan from the bank of space-time. This pure energy is momentarily converted into a particle-antiparticle pair. They don't stay apart for long, though. Being so close and electrically attracted to each other seals their fate. Not soon after do they recombine and release their energy back into space-time. It's very strange how the two were exact equals and opposites. Equal in mass, yet opposite in this thing called charge. Similar to the poles of a magnet, same poles repel, opposites attract. According to the wave function, if height represents magnitude of mass, then charge is angle or direction of the wave. Opposite charges means oppositely pointing waves. When these two waves overlap in place, they destructively interfere and cancel out their mass-wave, turning into pure energy in the form of photons.

Photons are interesting little things. They are pieces of some substance, yet they have no mass. What can be something and nothing at the same time? If we interpret the photon's wave function as being a dual-wave which points in both directions at the same time, then it interacts with the waves of mass as a massless entity. This is akin to Schrodinger's Cat, where the cat is both alive and dead inside the closed box. Two equal waves repel, opposites attract, and dual waves are neutral. They exist in a combined state of being as a tiny piece of matter-antimatter wave. This makes sense because before annihilation, both the matter and antimatter wave were in the same place at the same time. Two huge and tall waves pointing in opposite directions at maximum proximity, before the effects of quantum law took hold. Energy is just tiny pieces of combined matter-antimatter. Matter is just tiny pieces of half-energy. When matter combines with antimatter, the tiny pieces of energy are reassembled into their dual-wave form and explode outward.

So if by combining matter and antimatter gives us pure energy as photons, how can we combine photons to create the matter-antimatter pair? One interesting way I came up with was what I call the super massive photon. Its quantum state is a giant dual-wave, exactly like the state of being before annihilation. Except this time, this is the state before creation. Before the super massive dual-wave reaches a critical energy threshold and tears itself apart. The two halves are the individual up or down pair of matter-antimatter waves. But how does one tear apart a super massive photon? It may have something to do with the compactified dimensions of the Calabi-Yau space. Circumnavigation at great speed could carry enough angular momentum to tear apart the waves. Another way I thought about was the angular momentum with a photon's polarity. This would only work with a collapsing cloud of smaller photons. As the clump shrinks, it picks up speed in its rotation and flings itself apart.

How can a cloud of photons collapse into a larger one? A good question, and could be done through a process of quantum entangling in condensed matter physics. Assuming all particles are really tiny snippets of waves, the speed of collision is also affecting interaction time. At normal temperatures, atoms bounce off each other at a high enough speed that their tiny little wave parts don't have time to interact and behave like solid objects. But slowing them down by cooling allows the interaction time to be long enough for the tiny wave parts to mingle in the way of waves. When most of the little waves get close together, they overlap to constructively interfere into a single giant particle wave. Much in the same way swimming at the beach, when we see two smaller waves overlap and converge, they create a bigger version of the starting ingredients. So, if a cloud of photons are condensing and entangling, they all start to form a giant wave out of the smaller ones. And in this case, a giant dual-wave.

What can cause a cloud of photons to suddenly condense? Well, this is going out on a limb, but perhaps through some relation to rogue wave theory, a rolling sea of ultracold photons are hanging just outside our plane of existence, along one of the other cross sections of the Calabi-Yau manifold. According to this rogue wave theory, random quantum convergence can predict with a certain probability the occurrence of surrounding swells suddenly donating wave-energy to single one. This is the cause of the 30 meter waves that we see in the ocean. When scientists used fancy radar satellites and mapped the swells over the globe, they found that about 5 rogue waves of 100 feet high exists at any one time. This is randomly scattered throughout the entire ocean, having no pattern. So, maybe a rogue wave of photons quantum entangle to create a super massive photon, which then reaches a critical angular momentum and tears itself apart, to create the matter-antimatter pair. Or, perhaps this can be disproved through Occam's Razor.

Considering how protons emit photons when they fuse, this can explain the nature of instability. If a critical energy level was reached when a super massive photon tore apart, then a single stable proton has a minimum amount of photons as mass. During the fusing process, emitting photons makes the two unstable and they unite to satisfy the vacuum for energy. They stick to equalize their instability, since both have fewer photons than they should.

Why is it that people think that curvature must happen in a higher space? ALL SPACE IS CURVED. It's an intrinsic feature of space.

When things travel at a higher speed, they do not get heavier. That's not the way that relativity works. What happens is that the 'apparent weight' to a stationary observer is larger. Likewise, lorentz contraction and fitzgerald expansion, is only apparent to a stationary observer. That's why it's called 'relativity': you can't tell how fast you are travelling against a background.

You should understand that the model of gravity is due to the tension of space. Masses cause space to be less curved near them, which means that there is more length on one side of the circle than the other. As a result of tension of space, the straight line divides the length, not the angle, so the straight line appears to curve across the space. This is an illusion: there is no curve - that's the way straight lines go.

Photons have no mass, because they travel at the speed of light. A particle with mass can not do that. They do have energy, though, and momentum, and one can use these to get an 'indicated mass'. However, one does not use indicated mass. They're quantum particles in any case, so if you managed to join photons, (ignoring the spin issue), you get something that has a higher frequency,

The dream you dream alone is only a dream
the dream we dream together is reality.

So what you are saying is, that the gold nucleus inside a particle collider doesn't actually increase in mass itself, it only looks that way to an outside observer? I understand that when the two nuclei collide, the end result has more mass that the starting ingredients. Similar to colliding two mopeds together and they create a tank for very short amount of time, which then decays and explodes into a particle zoo. The energy of momentum is directly converted into energy of mass.

The relativistic increase in mass was thought to be done by the so called " electromagnetic mass". That is, a charged object is heavier and harder to move. A large object of normal size is heavier when it's charged or ionized. This was thought to be the main component as one gets close to c. That this extra mass was what increased.

You wouldn't happen to be from Iceland are you? I only ask from the use of the symbol for the letters "th". I recognize it a being used in Icelandic. This means I read the page you recommended. I like the ideas, makes sense.

I guess the thing I was trying to point out was comparing the increase of speed in a straight line as being similar to changing direction at constant speed. And, how the two scenarios could be the same given that the change of direction happens in a higher dimension of space. I understand that all of space is curved, I'm comparing trajectories along different axes. Let's say we're travelling due north at constant speed and point our car a few degrees to the east. We go around a small bend, feel the little bit of acceleration from going around the corner, and now have less displacement going north. Our slanted angle is pointing less north and a little east.

If space is the east-west direction, then driving due north is similar to moving along time while sitting still in space. We can travel north indefinitely and never move in an east-west direction. Just like with time, we can stand still in space indefinitely,but are constantly moving through time. Pointing a few degrees east is similar to when we start moving in space. We feel this little bit of acceleration when increasing speed in a straight line. This effect can be made by taking a curved path along our direction through time, and pointing a few degrees into space. Our slanted angle through space-time creates the illusion of velocity. As the now-moment cross section moves along space-time, the position of a point along the slanted line changes with respect to the cross section, giving the appearance of movement.

The effects of straight line acceleration can be explained by moving at constant speed around a curved path along time. Taking this corner in time points ourselves in a direction towards space. And by traveling through space, we travel a little less through time. Changing our direction through time meant we had to go around a bend. When going around a bend on the highway, we feel the same pulling force just like increasing speed in a straight line. But this time it happened at constant speed. We still increase our speed when changing direction: it's our eastern displacement. Angling more towards east means we travel more distance going east per unit of time. Angling more towards space means we travel more distance through space per unit of time. And in both circumstances, we still went around a corner and felt the pulling force of acceleration.

This is what is so interesting about standing on the surface of our planet. It feels like I'm accelerating straight up, feeling this pulling force in a downward direction. It's like I'm increasing speed at 22 mph per second, yet standing still. Due to the 13 trillion trillion lbs of this 8,000 mile wide object, space is literally bent in a curved direction toward the planet. We are on the bottom of this gravity well of curved space. This constant curvature is approaching our vector through time at an angle, and thus feels like we are going around a corner in time. Another situation where we feel a pulling force from curvature.

The th is a letter which disappeared in english only recently. You still see traces of it in things like 'ye old etea shoppe', where Y is a modern rendering of the capital. I am from australia.

The mass of particles is so well known that if you add the alpha-particle to two electrons mass (which gives He4), its heavier than the helium atom by the energy necessary to ionise it. Even chemical reactions convert mass into energy.

The dream you dream alone is only a dream
the dream we dream together is reality.

You know, I remember a while back playing around with the masses of a proton, neutron and electron. When I subtracted the mass of a neutron with that of a proton, it came out to be 2.5 x the mass of an electron, more or less. That is Mn-Mp = 2.5Me. I found that interesting. Seems like the neutron is neutral because it is a proton combined with a few electrons. And if this is the case, then protons stick to neutrons ( by the weak nuclear force) because they are feeling the electron part inside the neutron. This looks a lot like the electroweak theory acting out. Being that at a high enough energy, the electromagnetic and weak forces unite, this is how they are working at normal temps when separated. Interesting, huh?

The excess in mass between say a neutron and a proton+electron, or between a tritium nucleus and a Helion nucleus + electron, is emitted as energy, including photons. It's the source of energy of the sun, really.

The dream you dream alone is only a dream
the dream we dream together is reality.

That is true. So, what do you think about that? Do protons absorb, or become entangled in some way with electrons to create neutrons? It kind of makes sense. When the two combine, they neutralize the electric charge and become a heavier object. And when a proton gets close enough, it interacts with the electron that is still "bouncing around" inside, so to speak. The electron energy wave is entangled with the proton's wave, yet still maintains an identity. If the electroweak force arises when the weak nuclear and electromagnetic unite, then at normal temps (273 K) proton-neutron interaction happens because of an electron.

It can also relate to neutron stars after a nova. All remaining electrons will have combined with the remaining protons, leaving the degenerate matter behind. And beyond that, is a singularity. But, perhaps a theoretical quark-gluon star can be misinterpreted as a black hole, as quarks do not interact with photons. They would still have a powerful gravity well that is centered around an invisible object.

By "all space is curved", are you saying that space is in the shape of a glomochorix or bollochorix? If this is the case, then it would make sense that a gravity well ( especially two of them in proximity) would flatten the curvature a bit in the way you are saying. If it is hyperbolic, then it would also make sense that galaxies have the appearance of accelerating away. They're not actually moving away, space is curved hyperbolically and creates this illusion. I have thought it to be this way for a while.

"All space is curved", means that curvature is something that you can measure without going outside of it. Even euclidean space (horochorix) is curved (it has zero curvature). In hyperbolic geometry, the horocycle and horosphere are noticably round things. You can have what would in normal euclidean space be a tiling of hexagons, three at a corner (ie x6o3o), or a tiling of squares, four at a corner (x4o4o), and in hyperbolic space, you can have the angles between each of the hexagons and squares as right-angles!

A flat line in non-eucliedan geometry is not one that has zero curvature, but the same curvature as the space it passes through. So in hyperbolic geometry, the zero-curvature line is not a flat line - you have 'negative curvature' lines, one of which is minimal (ie nearest minus infinity).

As for entanglement etc, I generally don't believe that. What happens is that the proton and neutron are both spin-half particles, made from three quarks. It's just that the proton (ddd) is more stable than the neutron (ddu). When you get a mob of particles together, then it's more stable to have a mix of particles, so a tightly bound 'ddd' can decay into 'ddu' by the emission of some energy, which with charge, settles into a different potential well called an electron. Some other bits are emitted, because the electron is also a spin-half particle, and you need an even number of these.

With neutron stars, gravity is strong enough to collapse the nuclear cloud, and the atom consist collapses into the nucleus. What you get is a very large atom, with lots of protons, and many more neutrons. There may be other particles in the mix too, since the mass might permit something like duu or uuu to become stable.

Quark soup is when the little bubbles of three and two break up, so you get great masses of loose quarks. Not much is known about this, but i think that six quarks in a bag is unstable, rather like five and eight nucleids. (protons + neutrons). These are the things that saved the universe.

The dream you dream alone is only a dream
the dream we dream together is reality.

Wendy, you are one of the most amazing people I've ever informally met. You have an incredible wealth of knowledge, over many different topics. You blew my mind with the 1-dimensional torus. I didn't know my mind could be expanded into lower dimensions, but some how you did it. I thought that once I understood what a line was, I was done with the first dimension. I had to meditate on the links and chains, but I get it. I had no idea that there was a mathematical way to explain such things.

I am also a strong linguistic person. There always is a precise word for every definition. I remember reading those names you have for the different surface elements and such years back. I wanted to know the thought process and etymology for the terms. You quite clearly are the reference for it. Please forgive me if I offended you in any way with the stupid names of the shapes. Yours are the REAL names, derived through sound, academic sources. I am highly receptive to everything you have to teach.

As of yet, I have only read what I've learned, other than what I've figured out on my own. You offer an interactive way for me to learn, and it's very important to me. I think that the thirteen years I've been a bicycle mechanic has given me good logical problem solving and visualization. Perhaps a worthy predisposition for conceiving what's to be learned on this forum. It's crazy, though, I dropped out of high school and worked in bike shops since 18. And, here I am helping Keiji with the missing elements of a cylconinder! Something's not right here! I guess it's time to go back to school, whenever I can muster that.

Do you have any interest with pre-Sumerian archaeology? I have never cared about history, EVER. Until I found some sources that show ancient vikings living in Michigan 7,500 years ago. These people were working with forged metal tools, open pit copper mines, and making clay tablets with cuneiform and hieroglyphs. These tablets tell stories of Noah's flood and his three sons, the Tower of Babel, a global society, and so forth. Reading about the Bosnian Pyramid of the Sun, where 30,000 year old interlocking stones and pre-sanskrit writing are found. The strange 17,000 year old stone artifact, with a ball bearing of chrome steel inside it. The rapidly confiscated artifacts found in northern California, where metal plates had structural diagrams of aircraft on them were found, to name a few. The list goes on. So, go figure that when I learned human societies had a high knowledge and high technology several thousand years ago, I become fascinated with history. But, this history I probably won't be able to learn, through the means of certain academic grants and professionals being discredited with these breakthroughs. Perhaps in time.

It's only a hobby i do, usually at the keyboard. I mainly toy with weights and measures. Alicia Boole Stott (who did the heavy lifting associated with finding the uniform polytopes), i shalln't imagine, had fancy schooling in mathematics.

I basically am retired now, but i spent a life supporting a payroll computer interface, back in the dark old days of paper forms and punched cards. I wrote my first OS on punched tape, for goodness sake.

Still, calculus is largely beyond me, and most of this trig sutff is best avoided. One can still develop things like hyperbolic geometry if one tries. It's just a matter of dropping a few obvious restrictions (like the longest side of a tringle is shorter than the sum of the other two). In the main, one attacks space with a crooked ruler.

It's useful to look at dover reprints. Something like Coxeter's 'regular polytopes', is relatively inexpensive, and well worth the read. Lots of the mathematics can be skipped, but there is some useful stuff in there. It's the one i read first.

The dream you dream alone is only a dream
the dream we dream together is reality.

Punched tape, no way! But, nothing can outlive good ole' mechanical computers. When electronic fails, mechanical prevails. The Antikythera device is a great example.

Just read an article about a team of scientists sending a robotic probe into the Chernobyl area. In the highest and deadliest radiation zones, they discovered a fungus that converts gamma rays into energy. The fungus has melanin in it, and when gamma rays strike, the chemistry is altered and releases energy. This fungus uses melanin exactly how plants use chlorophyll to convert sunlight. This also strengthens the case of the panspermia theory, where life comes from outer space from native extremophiles.

ICN5D wrote: This brings me to a curious question: what is the constant speed that we are travelling through time? There can only be one answer to that one, and it has to be the speed of light, c. When we sit still at a traffic light, we have zero displacement in space. This is similar to driving due north, you have no east-west displacement. By taking a corner and driving NE, we feel this pull of acceleration, change our direction and add some displacement going east. We travel less distance going north now because we have given it to going east. So, if the magnitude of our vector through time is c, then changing direction in time and going around a corner will point us towards space. Pointing towards space is how we move, by removing our speed through time and adding it to space. This is how Einstein's Theory of Relativity fits in. The faster we go in space, the slower we move through time. Rotating the vector and reaching the speed of light in space means we remove all displacement through time. This is infinite velocity since travelling x miles in 0 hours is x/0, no solution, infinitely large.

Actually, going faster in space means going faster in time. The 4-velocity squared is dx2 - c2dt2 = constant. If |dx| increases, then |dt| must also increase to keep this constant. Contrast this with spatial rotations, where x2 + y2 = constant. If |x| increases, then |y| must decrease.

Here are some videos, just in case you haven't seen hyperbolic rotation before. This makes two perpendicular vectors move towards each other in a "scissors" motion.

Acceleration can indeed be thought of as curvature in time. A curve with constant curvature is: in Euclidean space, a circle; in Lorentzian spacetime, a hyperbola with asymptotes sloping at lightspeed; in Galilean spacetime, a parabola, the limit of a hyperbola as its asymptotes flatten (lightspeed is infinite).

I also found this interesting: "Newtonian spacetime is curved". It involves tensor calculus (watch the previous lectures if you want to learn), but it's still mostly understandable. A thrown object falling in Newtonian gravity can be treated as "straight line" (geodesic) motion in curved spacetime. It is critical to include time geometrically; gravity cannot be treated as geodesic motion in curved space.

So, let's take this rubber sheet and curl it up so we can join the ends. Now, inside this rubber tube is where the bowling ball is rolling around in a circle. This is a simplified version of moving through the compactified Calabi-Yau manifold. Since travelling a straight line also cycles around the curved extensions, the bowling ball circles around inside the tube by analogy. Picking up speed effects both the extended and curled up.

I don't know anything about string theory, but this looks incorrect. The point of having "extra dimensions" is to allow the straight line motion and the circular motion to be independent. The manifold can be completely flat in the first few dimensions (even on the small scale), and curved in the other dimensions.

mr_e_man wrote:Actually, going faster in space means going faster in time. The 4-velocity squared is dx2 - c2dt2 = constant. If |dx| increases, then |dt| must also increase to keep this constant.

I have always found this aspect confusing. I ask rhetorically, what does it mean that dt is increasing? It means that the observer's clock dt is measuring the time dt' takes to pass in the moving object's clock.

To me it seems more natural to keep dt constant. Then dt' is decreasing. It is of course the same thing, just a different perspective. So when no one is looking I think of it as time contraction.

Some people work with 1/t, which is called the celerity. But I don't know anything more about that. You would think it would be awkward. But it seems more natural in some ways.